SOIL MECHANICS - CHAPTER 10 doc

Chapter 10

FLOW NET

10.1 Potential and stream function

Two dimensional groundwater flow through a homogeneous soil can often be described approximately in a relatively simple way by a flow net,

that is a net of potential lines and stream lines. The principles will be discussed briefly in this chapter.

The groundwater potential, or just simply the potential, Φ is defined as

Φ = kh, (10.1)

where k is the permeability coefficient (or hydraulic conductivity), and h is the groundwater head. It is assumed that the hydraulic conductivity

k is a constant throughout the field. If this is not the case the concept of a potential can not be used. Darcy’s law, see (8.1), can now be written

as

qx = −

∂Φ

∂x ,

(10.2)

qz = −

∂Φ

∂z ,

or, using vector notation,

q = −∇Φ. (10.3)

In mathematical physics any quantity whose gradient is a vector field (for example forces or velocities), is often denoted as a potential. For

that reason in groundwater theory Φ is also called the potential. In some publications the groundwater head h itself is sometimes called the

potential, but strictly speaking that is not correct, even though the difference is merely the constant k.

The equations (10.2) indicate that no groundwater flow will flow in a direction in which the potential Φ is not changing. This means that in

a figure with lines of constant potential (these are denoted as potential lines) the flow is everywhere perpendicular to these potential lines, see

Figure 10.1.

The flow can also be described in terms of a stream function. This can best be introduced by noting that the flow must always satisfy the

equation of continuity, see (8.2), i.e.

∂qx

∂x +

∂qz

∂z = 0. (10.4)

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